Online communities are the latest phenomena on the Internet. At the heart of each community lies a social network. In this paper, we show a generalized framework to understand and reason in social networks. Previously, researchers have attempted to use inference-specific type of relationships. In this paper, we propose a framework to represent and reason with general case of social relationship network in a formal way. We call it relationship algebra. This paper presents this algebra and then shows how this algebra can be used for various interesting computations on a social network weaved in the virtual communities.